In an attempt to minimize the computational cost and obtain the best possible result, it is necessary to use an adaptive method based on automatic step-size selection.
Numerical computation based on adaptive methods varies the step-size \(n\)  such that the local error can be uniformly distributed at each time step \(t_n\) . Such an approach is akin to using non uniform Chebyshev nodes in polynomial interpolation [1]}. Practical error estimates are necessary to choose the step-size \(n\)  sufficiently small to obtain the required precision of the numerical solution and ensure \(n\)  is large enough to avoid unnecessary computational work [2]}, [3]}, [4]}.
